A268036
Cubes of the prime factors (with multiplicity) of n add up to n.
Original entry on oeis.org
1096744, 2836295, 4473671462, 23040925705, 13579716377989, 119429556097859
Offset: 1
1096744 = 2^3 * 11^3 * 103 = 2^3+2^3+2^3+11^3+11^3+11^3+103^3.
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isok(n) = {my(f = factor(n)); sum(k=1, #f~, f[k,1]^3*f[k, 2]) == n;} \\ Michel Marcus, Feb 09 2016
A283449
Smallest composite that is not an n-th power, but can be written as the sum of the n-th powers of two or more of its distinct prime factors.
Original entry on oeis.org
870, 378, 107827277891825604, 178101, 594839010, 275223438741, 26584448904822018, 40373802, 420707243066850, 952809806744100
Offset: 2
For n = 2: 870 = 2 * 3 * 5 * 29 and 2^2 + 5^2 + 29^2 = 870. Since 870 is the smallest number that is not a square and can be written as the sum of squares of some of its distinct prime factors, a(2) = 870.
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nextrowcomb(rowarr) = my(k=#rowarr, i=0); while(rowarr[k]==1, rowarr[k]=0; i++; k--); while(rowarr[k]==0 && k > 1, k--); if(rowarr[k]==1, rowarr[k]=0; rowarr[k+1]=1; k=k+2; while(i > 0, rowarr[k]=1; k++; i--), for(x=k, k+i, rowarr[x]=1)); rowarr
a(n) = forcomposite(c=1, , if(!ispower(c, n), my(f=factor(c)[, 1]~, v=vector(#f)); while(1, my(s=0); for(k=1, #v, if(v[k]==1, s=s+f[k]^n)); if(s==c, return(c)); if(vecmin(v)==1, break, v=nextrowcomb(v)))))
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